Finite Group Databasebeta

← #13075348

Subgroups — #13075348

Order 1408.

612 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66947C211yesmaximal, characteristic, complemented
2C2×#66927C211yesmaximal, characteristic
3C11×#387C211yesmaximal, characteristic, complemented
4#10622604C211yesmaximal, characteristic, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622546C211yesmaximal, characteristic, complemented
8#10622285C211yesmaximal, characteristic, complemented
9#10622285C211yesmaximal, characteristic, complemented
10#10622285C211yesmaximal, characteristic, complemented
11#10622278C211yesmaximal, characteristic, complemented
12#10622278C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C22×D44C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C42×C11C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43#66947—24no—
44#66927—24no—
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C23×D11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C23×D11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C2×D44—22no—
69C2×D44—22no—
70C2×D44—22no—
71C2×D44—22no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44D414yes—
86C2×C4×D11—22no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C42×C11—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109Dic11⋊C4—22no—
110Dic11⋊C4—22no—
111#2709—111nomaximal, Sylow
112C23×C11C2411yescharacteristic
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11C2×D412yes—
140C22×D11C2×D412yes—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11C2×D412yes—
160C2×C4×C11#4112yes—
161C2×C4×C11#4112yes—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174D44—44no—
175D44—44no—
176D44—44no—
177D44—44no—
178D44—44no—
179D44—44no—
180C4×D11—44no—
181C4×D11—44no—
182C2×#127—111no—
183C2×#123—111no—
184#394—111no—
185#394—111no—
186#394—111no—
187#394—111no—
188#394—111no—
189#394—111no—
190#387—111no—
191#387D1111yescharacteristic, complemented
192#386—111no—
193#386—111no—
194#386—111no—
195#386—111no—
196#386—111no—
197C22×C11C22×D411yescharacteristic
198C22×C11C2×#4111yescharacteristic
199C22×C11C2×#4111yescharacteristic
200C22×C11H(5,𝔽2)11yescharacteristic
201C22×C11H(5,𝔽2)11yescharacteristic
202C22×C11H(5,𝔽2)11yescharacteristic
203C22×C11H(5,𝔽2)11yescharacteristic
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—22no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239Dic11—41no—
240Dic11—41no—
241Dic11—41no—
242Dic11—41no—
243C22×D4—111no—
244C22×D4—111no—
245C22×D4—111no—
246C22×D4—111no—
247C22×D4—111no—
248C22×D4—111no—
249C23×C4—111no—
250C23×C4—111no—
251#127—224no—
252#123—224no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4C2×D1111yescharacteristic
256C2×C4⋊C4C2×D1111yescharacteristic
257C2×C22⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C42C2×D1111yescharacteristic
272#95—111no—
273#95—111no—
274#95—111no—
275#95—111no—
276#95C2×D1111yescharacteristic
277#95C2×D1111yescharacteristic
278#95C2×D1111yescharacteristic
279#95C2×D1111yescharacteristic
280C2×C11#53411yescharacteristic
281C2×C11#54011yescharacteristic
282C2×C11#54011yescharacteristic
283C2×C11#54611yescharacteristic
284C2×C11#54611yescharacteristic
285C2×C11#55911yescharacteristic
286C2×C11#56011yescharacteristic
287D11—42no—
288D11—42no—
289D11—81no—
290D11—81no—
291C24—111no—
292C24—111no—
293C24—111no—
294C24—111no—
295C2×D4—114no—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—222no—
299C2×D4—222no—
300C2×D4—222no—
301C2×D4—222no—
302C2×D4—222no—
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—222no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1111yescharacteristic
325C22×C4C22×D1111yescharacteristic
326C22×C4C22×D1111yescharacteristic
327C22×C4C22×D1111yescharacteristic
328C22×C4C22×D1111yescharacteristic
329C22×C4C22×D1111yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C22⋊C4—222no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C42—22no—
349C11#270911yescharacteristic, complemented, Sylow
350C23—112no—
351C23—112no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23—221no—
359C23—221no—
360C23—221no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23C23×D1111yescharacteristic
379D4—444no—
380D4—444no—
381D4—444no—
382D4—444no—
383D4—444no—
384D4—444no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—444no—
416C2×C4—444no—
417C2×C4#433912yes—
418C2×C4D4×D1112yes—
419C2×C4#434312yes—
420C22—222no—
421C22—222no—
422C22—222no—
423C22—222no—
424C22—222no—
425C22—222no—
426C22—441no—
427C22—441no—
428C22—441no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22—441no—
435C22—441no—
436C22—441no—
437C22—441no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22—441no—
443C22—441no—
444C22—441no—
445C22—441no—
446C22—441no—
447C22—441no—
448C22C2×#433911yescharacteristic
449C22C2×D4×D1111yescharacteristic
450C22C2×#434311yescharacteristic
451C22#6704211yescharacteristic
452C22#6704211yescharacteristic
453C22#6704211yescharacteristic
454C22#6704211yescharacteristic
455C4—22no—
456C4—22no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—441no—
463C4—441no—
464C4—441no—
465C4—441no—
466C2—442no—
467C2—442no—
468C2—881no—
469C2—881no—
470C2#1062306611yescharacteristic
471C2#1062308111yescharacteristic
472C2#1062311611yescharacteristic
473C2#1062316111yescharacteristic
474C2#1062318411yescharacteristic
475C2#1062322911yescharacteristic
476C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#387C2
prime radicalC2×#66927C2
hypercenter#387D11
hypocenterC11#2709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #387

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#66947C2semidirect
3. C11×#387C2semidirect
4. #10622604C2semidirect
5. #10622604C2semidirect
6. #10622604C2semidirect
7. #10622546C2semidirect
8. #10622285C2semidirect
9. #10622285C2semidirect
10. #10622285C2semidirect
11. #10622278C2semidirect
12. #10622278C2semidirect
13. #10622278C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
191. #387D11semidirect
349. C11#2709semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#669472
C2×#669272
C11×#3872
#106226042
#106225462
#106222852
#106222782
#270911